Global mean sea level rise during the recent warming hiatus from

satellite-based data

Luu Q.H. a,b*, Q. Wu c, P. Tkalich d, and G. Chen c,e

a Department of Computer Science and Software Engineering, Swinburne University of

Technology, Victoria, Australia; b School of Interdisciplinary Sciences, Vietnam National University, Hanoi, Vietnam;c Department of Ocean Technology, Ocean University of China, Qingdao, Shandong, China;d Tropical Marine Science Institute, National University of Singapore, Singapore;e Laboratory for Regional Oceanography and Numerical Modeling, Qingdao National

Laboratory for Marine Science and Technology, Qingdao, Shandong, China;

*Corresponding author(s): hluu@swin.edu.au

Global mean sea level rise during the recent warming hiatus from

satellite-based data

Satellite remote sensing has provided an unprecedented opportunity to understand

the spatio-temporal change of the Earth’s climate system. In this study, we take

advantage of the oceanographic satellite-based data to examine the global mean

sea level rise during a transitional episode (1994–2003) referred to as the onset of

recent global warming hiatus. We remove the signals accounted for the El Niño-

Southern Oscillation, the Pacific Decadal Oscillation, and solar radiation using an

Empirical Orthogonal Function and multivariate regression analysis. The trend

estimates over the period 1993–2015 are significantly improved in accordance

with the reduction of uncertainty by a half. Our results associate the observed

deceleration of sea level rise during the onset with the climate oscillations. It

strengthens a conclusion deduced by an alternative approach using modelling,

whilst highlights the robustness of combining satellite-based datasets and climate

indices in a reliable statistical estimation.

Keywords: satellite observations; sea level anomaly; global warming

1. Introduction

Satellite remote sensing (SRS) has a wide range of applications in most Earth science

disciplines, from hydrology, geography, geology, and ecology to oceanography

(Cracknell and Varotsos, 2007; Hossain 2016). In understanding the climate change,

SRS has been becoming an indispensable element of climate system observations, e.g.

more than a half of Essential Climate Variables strongly relied on satellite observations,

thanks to its accuracy and nearly global coverage sampling across the Earth’s surface

(Nerem et al., 2010; Chen et al., 2010; Cracknell and Varotsos, 2011; Yang et al.,

2013). The SRS data can be integrated into climate models to simulate climate

dynamics and to project future scenarios, or be assimilated to reanalysis products and

observational datasets for uses in other direct and indirect applications (e.g., IPCC,

2013; Prakash et al., 2013; Zeng et al., 2015; Loew et al., 2017).

Being a visible manifestation of climate change, the global warming has been

evident since the late nineteen century from both, direct temperature observations and

complicated climate models. Over the period 1880–2012, the global mean surface

temperature rise was estimated at 0.85°C (IPCC, 2013). Albeit with divergence in the

regional trends, the warming tendency was observed virtually over the entire the Earth.

IPCC (2013) attributed the centennial warming mainly to the emissions of atmospheric

greenhouse gases. However, an unexpected slowdown in the surface temperature trend

was noticed in the 1998–2012 episode, which is often referred to as the recent global

warming hiatus. During this short period, the temperature escalation was only 0.05°C

per decade, which is 2–3 times weaker than projected (IPCC, 2013). Its existence casted

doubt on the argument that the intensification in greenhouse gas concentration is the

source of global warming through increasing the global temperature. Since the notion is

a key for understanding the mechanism of climate change (Meehl et al., 2012; IPCC,

2013), the apparent hiatus triggered extensive debates (Estrada et al., 2013; Rajaratnam

et al., 2015; Xie, 2015; Watson et al., 2016). In fact, a rigorous and comprehensive

understanding of the greenhouse contribution to climate change is unlikely available

(Kondratyev and Varotsos, 1995; Varotsos et al., 2014).

While much attention is paid to questioning the existence or elucidating the

mechanism of hiatus, there has been little focus to ascertain its signature on the ocean

(Cazenave et al., 2014). Being a tangible manifestation of climate change (Becker et al.,

2014), the sea level rise may give us a hint on the footprint of hiatus since it is

expectedly rising proportional to the temperature (Rahmstorf 2007; Vermeer and

Rahmstorf, 2009; Hay et al., 2015). Fingerprints of natural variability of the Earth’s

climate system are also immensely apparent in the variations of ocean surface (e.g.,

Church et al., 2005; Church et al., 2006; Prandi et al., 2009; Zhang and Church, 2012).

Climate fluctuations strengthen or weaken the annual variations of sea level by an

increment that may overwhelm the marginal contribution of the global warming (Zhang

and Church, 2012; Trenberth, 2015; Luu et al., 2015). In fact, trend aliasing induced by

natural variability can amount up to 80% of the total sea level rise rate at some regions,

such as in the west of the Philippines during the period 1993–2009, when in the middle

and the east Pacific Ocean it rose three times faster than the global rate (Zhang and

Church, 2012; Peyser et al., 2016). Hence, recent studies (Han et al., 2010; Calafat and

Chambers, 2013; Cazenave et al., 2014; Yi et al., 2015; Visser et al., 2015; Watson,

2016) suggested that short-term natural oscillations should be removed from the

observed long-term signals to reveal underlying sea level trends linked to the global

warming.

In the paper, we take advantage of standardised SRS-based datasets to revisit the

responses of global mean sea level to the alleged hiatus. To capture the transitional

formation of the phenomenon and to preserve the reliability of statistical estimations,

we uncover the rates masked by natural variability by discounting its dominant modes

from sea level signals after an Empirical Orthogonal Function analysis. We then remove

climate and non-climate data from the observed sea level change (1993–2015), which

excludes artifacts arising from numerical modelling parameterizations, and discuss the

trends during the onset period (1994–2003).

2. Data and method

2.1. Sea level data and climatic indices

We adopt the latest monthly mean sea level data from two SRS-based datasets. The

main analysis is conducted with the Archiving, Validation and Interpretation of Satellite

Oceanographic (AVISO) product (http://www.aviso.altimetry.fr/en/data.html) for the

period 1993–2015 at the high resolution of 1/4°×1/4°, which integrates outputs from

Saral, Cryosat-2, Jason-1 and 2, T/P, Envisat, GFO, ERS-1 and 2 and Geosat satellites.

Another SRS-based data (https://www.cmar.csiro.au/sealevel/sl_data_cmar.html) used

for cross-validation are provided by Commonwealth Scientific and Industrial Research

Organization (CSIRO) which combined measurements from TOPEX/Poseidon, Jason-1,

and Jason-2/OSTM satellites in a coarser resolution (1°×1°). We removed seasonal

cycles from both datasets, which are then subjected to a 5-month moving average

smoothing as suggested by Church and Zhang (2012). Data corrected for the glacial

isostatic adjustment (GIA) and inverse barometer (IB) are used in the analysis and

discussion.

Dominant climate indices having high correlation with sea level variability are

employed to derive the trend. They consist of the Pacific Decadal Oscillation (PDO),

the El Niño–Southern Oscillation (ENSO), the Central Pacific ENSO (CP-ENSO) and

the total solar irradiance (TSI). The monthly PDO index from 1854 was archived from

Extended Reconstructed Sea Surface Temperature delivered by the National Centers for

Environmental Information (https://www.ncdc.noaa.gov/teleconnections/pdo/). To

depict ENSO, we adopt the Multivariate ENSO Index (MEI,

http://www.esrl.noaa.gov/psd/enso/mei) provided by Wolter and Timlin (2011). The

CP-ENSO is another climate fluctuation alternative to the regular ENSO

(http://www.ess.uci.edu/~yu/2OSC/), which has a stronger teleconnection with the

southern Indian Ocean (Yu and Kao, 2007; Kao and Yu, 2009). Lastly, TSI represents

the influence of the Sun on the Earth’s climate system (Ridley et al., 2014), and is

prepared by Frohlich (2000) over the time span 1978–2015 at the Physikalisch

Meteorologisches Observatorium Davos of the World Radiation Center

(https://www.pmodwrc.ch/pmod.php?topic=tsi/composite/SolarConstant). We applied

the successive 25-month and 37-month moving averages to PDO and TSI as suggested

by Zhang and Church (2012) to yield corresponding decadal indices (namely, D1 and

D2, respectively); while the interannual and shorter-timescale ones (I1, I2, and I3)

related to ENSO and CP-ENSO are derived by subtracting the averages from respective

original time-series. Due to this smoothing, all data used are truncated to the common

period (1993–2012).

2.2. Principal modes of sea level variability and trend estimations

Empirical Orthogonal Function (EOF) analysis is employed to detect the principal

modes of sea level variability which are thereafter correlated to well-established climate

phenomena. Bearing in mind that the long-term sea level variability can be smeared up

by the strong short-term signal, we pay attention to both dominant decadal and

interannual components. The low-passed subset is deduced from successive 25- and 37-

month moving averages of the AVISO data, which is sufficient to resolve the decadal

contribution (Zhang and Church, 2012). The interannual and shorter timescale

component is deduced by removing the derived low-pass filter from the original data.

From the analysis, it was found in the decadal subset that the first two modes account

for 61.2% of the total variance. The most dominant mode (EOF1-D) explains 38.8% of

the signals and is highly correlated (correlation coefficient r=0.92) with the

corresponding low-passed filtered PDO; while the second mode (EOF2-D) is strongly

tied (r=0.78) to TSI. Meanwhile, three leading dominant modes in the interannual

subset are overwhelmed by signals related to ENSO which account for 38.6% total

variance. Explaining 25.9% total signals, the largest principal mode (EOF1-I) is tightly

connected (r=0.94) to the ENSO, while the second pattern (EOF2-I) bears a congruency

(r=0.90) with the lagged ENSO (shifted by 7 months). The remaining dominant mode is

linked to the CP-ENSO (r=0.56). By utilizing the EOF analysis with more dominant

components of natural variability, we extend the works of Zhang and Church (2012) to

better estimate sea level trends.

The fitting has been used intensively to separate the sea level rise rate unrelated

to global warming (Visser et al., 2015). In our multiple variable linear regression

(MVLR) analysis, we assume that sea level change (h) is proportional to temporal states

determined decadal and interannual climate indices and the trend (a) linked to the

global warming. Its relationship is expressed in the formula:

h ( t )=a t +∑k=1

2

dk Dk+∑k=1

3

ik I k+b+ε

(1)

where t is the time (month), Dk (k=1,2) and I k (k=1,2,3) are the above-defined

(normalized) decadal and interannual indices, dk , ik and b are the fitted coefficients, and

ε is the error (considered as random noise). In case the trend is uncorrected for the

climate variability, coefficients related to climate indices (dk,ik) are excluded, and the

MVLR is deducible to the single variable linear regression (SVLR) to compute only the

so-called apparent trend. We apply MVLR to remove climate signals in either a spatial

(i.e., two-dimensional) set of time-series of the regional sea level (RSL) or execute the

correction on the sole time-series of the global mean sea level (GMSL). The global

mean time-series derived with area weights from those both approaches, being named

correspondingly the RA (the global average of RSL) and the GA, show similar temporal

pattern but slightly different mean rates (Figure 3a).

Statistical estimations at 95% confidence interval are computed using a two-

tailed Student’s t-test. To resolve the autocorrelation problem arising from the original

least square fitting, we applied the first-order Auto-Regressive and first-order Moving-

Average (ARMA(1,1)) model suggested by Foster and Brown (2015), which correcting

the underestimation in the commonly used first-order autoregressive AR(1) models.

3. Global mean sea level trend and the signature of hiatus

3.1. Synoptic regional and global mean sea level trends

Spatial patterns of RSL trends derived from SRS-based observations are displayed in

Figure 1, which are consistent with the previous study of Zhang and Church (2012). In

the Pacific Ocean, the apparent trends computed from AVISO data (Figure 1a) consist

of significantly high RSL rise rates (>12 mm year-1) founded in the western tropical area

(20°S–20°N; 120°E–175°E). At its eastern basin, small apparent trends (-2–2 mm year-

1) extend from 30°S to 40°N latitudes, being the most prominent along the northern side

of the equator (5°N–20°N); while a parallelogram structure is also detected around

(5°S–18°N; 160°E–180°E). Corrected for the natural variability (Figure 1b), the areas

having highly confident rates have enlarged by 70%, seizing the central tropical region

of the Pacific Ocean. Our results thus bear a high similarity in terms of basic patterns

and magnitudes with the sea level footprints derived earlier by Zhang and Church

(2012).

The monthly change of GMSL records starting in 1993 is shown in Figure 2a.

The corrected GMSL in both averaging approaches (GA and RA) are similar, except for

few discrepancies (<4 mm) in the years 1997, 2008 and 2011. Meanwhile, the

differences between apparent GMSL and the corrected one are year-to-year and strongly

linked to the variability (Figures 2b, 2c, and 2d). The apparent GMSL lowered (~3–6

mm) in 1996, 2007–2008 and 2009–2010, while it was higher (by ~2–5 mm) in

1997/1998 (Figure 2a). They are often attributed to ENSO and PDO (Cazenave et al.,

2012; Meyssignac et al., 2012; Hamlington et al., 2013). For instance, a positive

anomaly (~5 mm) of apparent GMSL with respect to the corrected level was

experienced during the strong El Niño event in 1997/1998 (Figure 2b). It is consistent

with the finding of Cazenave et al. (2012) who pointed this to the mass change in the

tropical Pacific Ocean. Such results imply that our corrected sea level represents

effectively historic patterns and agrees well with previous regional findings.

3.2. Signature of hiatus in global mean sea level observations

To examine the signature of hiatus, we first estimate the recent evolution of the apparent

GMSL rise rates. The rates are calculated for different time spans, each of which starts

in a given year but altogether ends in 2012 (Figure 3a). It shows that there is a gradual

but hardly noticeable reduction in the apparent sea level rise rate from 3.18±0.29 mm

year-1 for the period 1994–2012 to the 2.98±1.53 mm year-1 in the more recent episode

2003–2012. Yet, there was no spike or discontinuity in sea level trend experienced in

either year 1997, 1999 or 2001. Although ocean volume is tied to the mean temperature

change mainly through two mechanisms (i.e., thermal expansion of seawater associated

with the increase in ocean heat content, and the melt of ice sheets and glaciers due to the

warmer atmosphere), the response of sea level to an abrupt change might be slower. For

volcano eruptions, aerosols injected into the stratosphere caused a scattering of

incoming solar radiation and a rapid cooling of the atmosphere, subsequently leading to

a rapid drop of the GMSL up to 5 mm in the case of the Mt Pinatubo incident in 1991

(Church et al., 2005). The fastest sea level drops are often observed between 6 to 18

months after the eruption events (Church et al., 2005). The manifestation of a slowdown

in sea level rise was probably faster, i.e., happening no later than 2002, since the

temperate variations in the hiatus may not undergo a process as complicated as in the

volcano eruption to influence the water mass. Taken this rule of thumb into account, we

observe marginal deceleration rate 0.7% per year in the apparent sea level during the

onset (1994–2003), but no abrupt change was visible in this era.

The alleged corresponding hiatus in sea level might be nevertheless masked by

the natural variability. By subtracting the climate fluctuations, we obtained the corrected

GMSL rise rate with the MVLR (Figure 3a). In the GA approach, the revised rate for

the period 1994–2012 is 3.32±0.14 mm year-1. It is almost unchanged for the latest era

2003–2012 with the rate of 3.28±0.68 mm year-1. In the RA approach, the global rates

become uniformly lower by about 0.08 mm year-1 on average. The corrected ones are

3.24±0.17 mm year-1 for the years 1994–2012, and 3.20±0.86 mm year-1 for 2003–2012.

In all suspicious years (1997, 1999 and 2001), there is no evidence of any abrupt

slowdown (>0.1mm year-1) in sea level rise. The corrected GMSL rise rates computed

by the MVLR method in the both approaches are similar around the crests being about

3.20–3.30 mm year-1 since 1993. They are higher than the apparent GMSL rate

regressed using the SVLR method by an amount of 0.10–0.35 mm year-1 during the

onset. The increasing gaps between them are mainly induced by the oblique tendency

caused by the combined strengthening of recent negative phase of PDO (Figure 2c) and

the intensification of ENSO events (Figure 2b), same as indicated earlier (Zhang and

Church, 2012; Hamlington et al., 2013; Kosaka and Xie, 2013; England et al., 2014;

Watanabe et al., 2014; Maher et al., 2014; Meehl et al., 2014; Trenberth, 2015). Again

we found that there is no sudden drop (>3%) of sea level tendency observed during the

entire onset period.

The uncertainty range remains relatively high in the SVLR analysis of the

AVISO data. For instance, the confidence level can be as large as ±55% of the estimate

of a trend for the recent 10 years (2003–2012). Thanks to the improvement in signal-to-

noise ratio, the introduction of natural variability into the MVLR regression reduced the

uncertainty down to ±20–30% of the overall trend during the same period. Between

1994 and 2003, longer time-series lead to the shorter (i.e. better) the confidence interval,

linked by a relationship that follows a logarithm-like fold. The enhancement in

estimation, on the other hand, is also attributed to the application of ARMA(1,1)

method, which helps to resolve the underestimated standard errors in the ordinary least

square fitting technique.

To examine the sensitivity related to the dataset used, we compared the

estimations with another source of SRS data provided by CSIRO, which is different in

terms of the number of satellites involved, the processing technique, and the spatial

resolution. Figure 1c shows the regional patterns of sea level change over 1994–2012

derived from the CSIRO data in which the natural variability is completely removed.

Their footprints and scales are identical, except that the CSIRO features look smoother

(Figure 1c) over the entire globe (as its resolution is 16 times coarser) and its rate is

smaller (Figure 3b). The transient variability of trend slightly meanders between 3.05–

3.35 mm year-1 in the period 1994–2003, but its overall feature is highly similar to the

AVISO where no statistically significant slowdown is spotted (Figure 3b). Since both

dataset CSIRO and AVISO shared similar patterns, we can extend the sensitivity tests

using prepared CSIRO data in order to inspect the impact of IB and GIA corrections on

the existence of slowdown. It is found that when the IB effect is not taken into account,

the GMSL rise rate increased from 3.25±0.29 mm year-1 for the period 1994–2012 to

3.40±0.82 mm year-1 over 2013–2012 with a gradual upward in trend. On the other

hand, the trends uncorrected for the GIA also have an accelerating tendency with a

marginally lower rate of 2.65±0.24 mm year-1 for the same years.

4. Discussion and conclusion

The sea level change is driven by a mixture of global (anthropogenic) trends and

regional (natural) variabilities. This study re-examines the GMSL trends in which the

climatic oscillations associated with ENSO, PDO and solar radiation are removed from

the recorded sea level signals. Thanks to the latest SRS-based measurements over the

period 1993–2015, we can analyze the GMSL changes during the onset of global

warming hiatus (1994–2003). It is found that despite corrected regional sea level trends

are non-uniform, the GMSL hardly exhibit any slowdown (>1mm year-1) during the

onset. Subtraction of climate variability from the recorded signal reduces trend

uncertainty by half.

Non-climatic factors have been known to influence significantly the long-term

sea level trend, including the contribution of terrestrial waters (Chao et al., 2008; Llovel

et al., 2011). We further roughly assess the influence of one of its major contributions,

the artificial reservoir water impoundment, to the sea level change by supplementing it

to the corrected GMSL (Figure 2a) and the tendency (Figure 3a). It is found that the

modified GMSL rise rates become slightly faster the period (1994–2012), reaching 3.58

mm year-1 and 3.50 mm year-1 for GA and RA approaches, respectively (Figure 2a).

However, the trend tendency is unlikely to change significantly (>5%) in the long-term

(Figure 3a).

In a recent report, Canezave et al. (2014) corrected for natural variability by

combing various sources of model outputs and data. They took advantage of the Gravity

Recovery and Climate Experience (GRACE) measurement to capture the variations in

ocean mass and terrestrial water storage for the period 2003–2011 and supplemented the

missing data over 1993–2003 by outputs combined from a hydrological model and a

thermal expansion dataset processed from Argo floats. Interestingly, their computed

rates are highly consistent with our estimates by marginal differences of only 2–5%

(which is mainly due to slightly different compared periods), rejecting the slowdown of

sea level rise. The similarity is understandable, since variations in ocean mass and

terrestrial water storage are modulated by dominant climate fluctuations (Llovel et al.

2011; Canezave et al., 2014; Becker et al., 2014). On the other hand, as the GMSL rise

is camouflaged by such variability, its apparent rate is expectedly higher after the onset

when dominant climate drivers reverse its phase. This anticipation was recently

confirmed by Yi et al. (2017) who compared the different apparent rates and budgets of

recent GMSL rise.

While the global mean temperature and sea level regularly rose in tandem

(Rahmstorf 2007; Wu et al., 2017), the relationship between them is stochastic, and

undeterminable out of the context of sophisticated Earth’s climate system. Influential

factors are pointed to thermal expansion of ocean waters, decreasing land water storage

and land ice melting (Yi et al., 2017). Continuing efforts are needed to give deeper

insights, for instance, into how the deceleration of temperature increase impacts the

global mean sea level rise, and to which extent its influence is weakened by the melts of

ice and terrestrial water storage during the onset.

In summary, our results are in favour of associating the deceleration of apparent

sea level rise during the onset of hiatus with the natural variability. Instead of relying on

complicated modelling computations, this study highlights an independent and efficient

approach that directly explores satellite-based datasets within a reliable statistical

estimation to understand the changing climate.

Acknowledgments

There are no financial conflicts of interests for all authors. We thank the editor and two anonymous reviewers for useful comments and suggestions. G.C. and Q.W. were supported by N.F.S. of China grants no. 41331172, U1406404 and G.C.A.S.I.P. grant no. 61361136001, GASI-03-01-01-09.

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Figure 1. Regional sea level trends deriving from satellite altimetry data for the period

1994–2012: (a) SVLR for AVISO dataset; (b) MVLR for AVISO; and (c) MVLR for

CSIRO dataset. Stippling indicates trend exceeding 95% confidence level. (d)

Meridional average sea level trends derived from AVISO data for different periods all

ending in the year 2012 with starting in 1994 (red), 1998 (green) and 2002 (blue). The

dashed lines show trends from SVLR, while the solid lines present rates derived by

applying MVLR on the RSL data.

Figure 2. (a) GMSL averaged monthly over the period 1993 to 2013 from AVISO data

under different unadjusted and unadjusted experiments. Monthly variability of

normalized climate indices: (b) high-passed MEI; (c) low-passed PDO; and (d) low-

passed TSI.

Figure 3. Transient variations of the GMSL rise rates over different periods, starting

from a year in between 1994 and 2003 and ending in the year 2012 derived from: (a)

AVISO data and (b) CSIRO data. For the CSIRO data, the pure trend is computed using

SVLR in the EXP1 case; while with EXP2 and EXP3 experiments, trends are corrected

for natural variability using the RA and GA approaches, respectively. Both EXP4 and

EXP5 experiments stem from EXP2, except that the IB effect is not considered in EXP4

while the GIA correction is not applied in EXP5. Vertical bars represent the 95%

confidence intervals.